Intervention Dauphine - Finance Quantitative - 25 mars 2021

1 - Import des librairies nécessaires

import os
import pandas as pd
pd.set_option('display.float_format', lambda x: '%.3f' % x)
import numpy as np
from datetime import date, datetime
from time import time
dateparse = lambda x: datetime.strptime(x, '%d/%m/%Y')

from IPython.display import display
from matplotlib import pyplot as plt

import plotly.offline as pyo
import plotly.graph_objs as go
pyo.init_notebook_mode()

from sklearn.model_selection import train_test_split


from aeqlib import viz, quantlib, lisa

FOLDER = 'data'

exx = pd.read_csv(
    f'{FOLDER}/stoxx50.csv',
    header=0, index_col=0, sep=';',
    parse_dates=True, date_parser=dateparse)

exx

	OR FP Equity	DG FP Equity	SAN SQ Equity	ASML NA Equity	PHIA NA Equity	FP FP Equity	AI FP Equity	CS FP Equity	BNP FP Equity	BN FP Equity	...	SAP GY Equity	RI FP Equity	ADS GY Equity	DTE GY Equity	DPW GY Equity	DAI GY Equity	DB1 GY Equity	VNA GY Equity	SX5T Index	SXXP Index
Dates
2005-01-03	56.450	24.594	8.085	11.860	19.357	39.624	35.179	17.635	51.786	32.555	...	32.895	43.614	30.230	16.710	17.270	35.680	22.325	NaN	4063.340	252.550
2005-01-04	56.900	24.840	8.085	11.640	19.063	39.476	35.179	17.549	52.123	32.743	...	32.250	43.729	30.075	16.840	17.060	36.050	22.400	NaN	4064.830	253.550
2005-01-05	56.950	24.741	7.971	11.310	18.681	39.106	34.792	17.319	51.834	32.507	...	32.050	43.999	29.700	16.700	17.000	35.920	22.300	NaN	4032.100	251.850
2005-01-06	57.300	25.085	7.971	11.290	18.671	39.402	34.895	17.444	52.605	32.672	...	32.675	43.845	29.838	16.710	17.050	36.110	22.370	NaN	4058.170	253.090
2005-01-07	57.850	25.208	7.936	11.240	18.622	39.526	35.127	17.568	53.232	32.956	...	33.335	43.999	29.663	16.780	17.150	35.930	22.300	NaN	4076.730	254.720
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-01-22	296.300	80.460	2.581	462.900	45.635	36.220	132.050	19.212	43.085	54.560	...	104.700	153.100	278.000	15.065	42.820	59.070	132.900	55.060	7812.310	408.540
2021-01-25	299.000	78.720	2.490	461.350	46.690	35.350	131.400	18.770	41.230	54.700	...	105.520	151.950	269.000	14.920	42.220	57.440	133.000	55.860	7705.460	405.130
2021-01-26	301.800	77.980	2.533	458.550	47.235	35.980	134.950	18.856	41.990	55.380	...	109.980	153.900	276.700	14.990	42.960	58.890	134.450	55.760	7791.520	407.700
2021-01-27	297.600	76.840	2.433	440.650	46.840	35.825	136.500	18.674	40.525	55.200	...	109.640	152.950	270.700	15.085	41.560	57.250	132.800	55.220	7669.110	402.980
2021-01-28	297.700	77.980	2.397	436.650	46.290	35.365	135.050	18.424	40.095	55.100	...	107.660	156.400	269.800	14.900	41.400	56.470	133.050	55.400	7625.060	399.090

4194 rows × 52 columns

2 - Stratégie quantitative simple

Définition de la moyenne mobile simple - Simple Moving Average (SMA) - $SMA_{n, t} = \frac{1}{n}\sum_{0}^{n-1} P_{t-i}$

def moving_average(s, window=10):
    return(s.rolling(window=window).mean())

def crossing_sma_strategy(s, w1, w2, shift=0):
    sma1 = moving_average(s, w1)
    sma2 = moving_average(s, w2)
    signal = np.sign(sma1 - sma2).diff() / 2
    signal = signal.shift(shift)
    signal = signal.replace(0, np.nan)
    signal.iloc[0] = 1
    signal = signal.pad()
    return(signal)

asset = exx['SX5T Index']

s = asset.copy()
w1 = 200
w2 = 500

sma1 = moving_average(s, w1)
sma2 = moving_average(s, w2)
signal = np.sign(sma1 - sma2).diff() / 2

# example of strategy with 200 and 500
sig = crossing_sma_strategy(asset, 200, 500)
strat = (sig * asset.pct_change().fillna(0) + 1).cumprod() * asset.iloc[0]

# plot
name = asset.name
all_windows = [1, 5, 10, 12, 50, 100, 200, 500]
df = pd.concat([moving_average(asset, w) for w in all_windows], axis=1)
df.columns = [f'{name}_SMA_{w}' for w in all_windows]
fig = viz.easy_plot(pd.concat([df, strat], axis=1), show=False)

fig.show()

def sma_strategy_wrapper(s, w1, w2, fees=0.0005, shift=2):
    sig = crossing_sma_strategy(s, w1, w2, shift=shift)
    strat = (sig * s.pct_change().fillna(0) - abs(sig.diff().fillna(0)) * fees + 1).cumprod() * s.iloc[0]
    return strat.iloc[-1] / strat.iloc[0] - 1

Grid-search avec échantillonnage aléatoire

Test sans fees ni shift, puis avec fees, puis avec shift

from itertools import product
m = range(1, 501)

for func in [
    lambda w: sma_strategy_wrapper(asset, w[0], w[1], fees=0, shift=0),
    lambda w: sma_strategy_wrapper(asset, w[0], w[1], fees=0.0005, shift=0),
    lambda w: sma_strategy_wrapper(asset, w[0], w[1], fees=0, shift=2),
    lambda w: sma_strategy_wrapper(asset, w[0], w[1], fees=0.0005, shift=2),
]:
    grid = pd.DataFrame(product(m, m)).sample(frac = 0.01, random_state=3)
    grid = grid.sort_index()
    t1 = time()
    grid['results'] = grid.apply(
        func,
        axis=1)
    t2 = time()
    print(t2 - t1)

    display(grid.sort_values(by='results'))

14.747560262680054

	0	1	results
5000	11	1	-1.000
32000	65	1	-1.000
92000	185	1	-0.992
124500	250	1	-0.992
137500	276	1	-0.985
...	...	...	...
1516	4	17	27.731
309	1	310	27.927
2006	5	7	39.985
251	1	252	85.900
7	1	8	5661766894.088

2500 rows × 3 columns

11.619581937789917

	0	1	results
5000	11	1	-1.000
32000	65	1	-1.000
124500	250	1	-0.993
92000	185	1	-0.993
137500	276	1	-0.987
...	...	...	...
339	1	340	21.689
338	1	339	22.711
309	1	310	24.857
251	1	252	73.531
7	1	8	2446296971.245

2500 rows × 3 columns

10.17225193977356

	0	1	results
14536	30	37	-0.855
7	1	8	-0.850
5065	11	66	-0.839
236495	473	496	-0.838
214996	430	497	-0.834
...	...	...	...
249953	500	454	2.246
216814	434	315	2.315
217314	435	315	2.351
248441	497	442	2.636
249439	499	440	3.204

2500 rows × 3 columns

10.679455995559692

	0	1	results
7	1	8	-0.936
2006	5	7	-0.880
14536	30	37	-0.876
5065	11	66	-0.854
236495	473	496	-0.842
...	...	...	...
249953	500	454	2.198
216814	434	315	2.289
217314	435	315	2.324
248441	497	442	2.582
249439	499	440	3.150

2500 rows × 3 columns

print(sma_strategy_wrapper(asset, 1, 8, fees=0.0, shift=0))
print(sma_strategy_wrapper(asset, 1, 8, fees=0.0005, shift=2))

5661766894.087999
-0.9358196371136654

grid['results'].describe(percentiles=np.linspace(0, 1, 11))

count   2500.000
mean       0.025
std        0.501
min       -0.936
0%        -0.936
10%       -0.518
20%       -0.423
30%       -0.326
40%       -0.230
50%       -0.105
60%        0.078
70%        0.280
80%        0.466
90%        0.713
100%       3.150
max        3.150
Name: results, dtype: float64

grid.sort_values('results')

	0	1	results
7	1	8	-0.936
2006	5	7	-0.880
14536	30	37	-0.876
5065	11	66	-0.854
236495	473	496	-0.842
...	...	...	...
249953	500	454	2.198
216814	434	315	2.289
217314	435	315	2.324
248441	497	442	2.582
249439	499	440	3.150

2500 rows × 3 columns

tol = 20
grid.loc[(abs(grid[0] - 499) < tol) & (abs(grid[1]-440) < tol)]

	0	1	results
240450	481	451	0.821
242439	485	440	1.710
242446	485	447	0.447
243924	488	425	2.121
244922	490	423	1.984
244954	490	455	0.742
246950	494	451	1.433
246957	494	458	1.553
247422	495	423	1.649
248441	497	442	2.582
249439	499	440	3.150
249953	500	454	2.198

En séparant échantillon de test d'échantillon d'apprentissage...

def optimize(asset, w_min, w_max):
    
    train, test = train_test_split(asset, test_size=0.2, shuffle=False)
    
    m = range(w_min, w_max+1)
    grid = pd.DataFrame(product(m, m)).sample(frac = 0.01, random_state=3)
    grid = grid.sort_index()
    grid['results'] = grid.apply(lambda w: sma_strategy_wrapper(train, w[0], w[1], fees=0.0005, shift=2), axis=1)
    best = grid.sort_values('results', ascending=False).iloc[0,:]
    w0, w1, IS_results = best
    print(w0)
    print(w1)
    complete_result = sma_strategy_wrapper(asset, int(w0), int(w1))
    return grid, IS_results, complete_result
    

grid, IS, complete = optimize(asset, 5, 500)

52.0
143.0

# example of strategy with 200 and 500
w1 = 52
w2 = 143
shift=2
fees = 0.0005

sig = crossing_sma_strategy(s, w1, w2, shift=shift)
strat = (sig * s.pct_change().fillna(0) - abs(sig.diff().fillna(0)) * fees + 1).cumprod() * s.iloc[0]
train, test = train_test_split(s, test_size=0.2, shuffle=False)

# plot
name = asset.name
all_windows = [1, 52, 143]
df = pd.concat([moving_average(asset, w) for w in all_windows], axis=1)
df.columns = [f'{name}_SMA_{w}' for w in all_windows]
fig = viz.easy_plot(pd.concat([df, strat], axis=1), show=False)
fig.add_vline(x = train.index[-1])
fig.show()

3 - Application du Machine-Learning : clustering

def identity(stock, benchmark='SX5T Index'):
    bmk = exx[benchmark]
    stock_clean = stock.pct_change().dropna()
    bmk_clean = bmk.pct_change().dropna()
    
    stock_1y = stock_clean.tail(252)
    stock_3y = stock_clean.tail(3 * 252)
    
    bmk_1y = bmk_clean.reindex(index = stock_1y.index)
    bmk_3y = bmk_clean.reindex(index = stock_3y.index)
    
    ids = []
    for w, stock_, bmk_ in zip([1, 3], [stock_1y, stock_3y], [bmk_1y, bmk_3y]):
        perf = quantlib.annualized_return(stock_)
        vol = quantlib.volatility(stock_)
        sharpe = quantlib.sharpe_corrected(stock_)
        semi_vol = quantlib.semi_volatility(stock_)
        sortino = quantlib.sortino_corrected(stock_)
        calmar = quantlib.calmar_corrected(stock_)
        mdd = quantlib.max_draw_down(stock_)
        var = quantlib.value_at_risk(stock_.to_frame()).iloc[0]
        cvar = quantlib.expected_shortfall(stock_.to_frame()).iloc[0]
        tracking = quantlib.tracking_error(pd.concat([stock_, bmk_], axis=1), stock_.name, bmk_.name)
        information = quantlib.information_ratio(pd.concat([stock_, bmk_], axis=1), stock_.name, bmk_.name)
        beta = quantlib.beta_ptf(pd.concat([stock_, bmk_], axis=1), stock_.name, bmk_.name)
        alpha = quantlib.alpha_ptf(pd.concat([stock_, bmk_], axis=1), stock_.name, bmk_.name)
        up_days = quantlib.up_days_ptf(pd.concat([stock_, bmk_], axis=1), stock_.name, bmk_.name)
        
        identity = pd.Series({
            "perf": perf,
            "vol": vol,
            "sharpe": sharpe,
            "semi_vol": semi_vol,
            "sortino": sortino,
            "calmar": calmar,
            "mdd": mdd,
            "var": var,
            "cvar": cvar,
            "tracking": tracking,
            "information": information,
            "beta": beta,
            "alpha": alpha,
            "up_days": up_days
        })
        identity.index = [f'{ind}_{w}y' for ind in identity.index]
        ids.append(identity)

    return pd.concat(ids)

all_ids = exx.iloc[:, :-2].apply(identity, axis=0)

all_ids.T.sort_values('perf_1y')

	perf_1y	vol_1y	sharpe_1y	semi_vol_1y	sortino_1y	calmar_1y	mdd_1y	var_1y	cvar_1y	tracking_1y	...	sortino_3y	calmar_3y	mdd_3y	var_3y	cvar_3y	tracking_3y	information_3y	beta_3y	alpha_3y	up_days_3y
AIR FP Equity	-0.385	0.737	-0.284	0.681	-0.262	0.247	-0.641	-0.129	-0.176	0.556	...	-0.021	0.031	-0.647	-0.087	-0.130	0.352	-0.233	1.536	-0.000	0.451
SAN SQ Equity	-0.368	0.584	-0.215	0.552	-0.203	0.225	-0.611	-0.099	-0.131	0.387	...	-0.086	0.166	-0.724	-0.059	-0.092	0.264	-1.004	1.401	-0.001	0.430
ENI IM Equity	-0.360	0.520	-0.187	0.563	-0.203	0.198	-0.551	-0.070	-0.153	0.309	...	-0.054	0.096	-0.649	-0.058	-0.098	0.209	-0.877	1.241	-0.001	0.440
BAYN GY Equity	-0.352	0.423	-0.149	0.439	-0.155	0.169	-0.480	-0.071	-0.118	0.277	...	-0.069	0.118	-0.610	-0.051	-0.095	0.251	-0.909	1.079	-0.001	0.450
INGA NA Equity	-0.332	0.628	-0.209	0.625	-0.208	0.200	-0.603	-0.094	-0.144	0.411	...	-0.084	0.144	-0.703	-0.081	-0.109	0.277	-0.864	1.511	-0.001	0.451
SAF FP Equity	-0.288	0.712	-0.205	0.689	-0.198	0.184	-0.639	-0.151	-0.187	0.512	...	0.137	-0.093	-0.646	-0.077	-0.133	0.326	0.078	1.537	0.000	0.475
ISP IM Equity	-0.285	0.441	-0.126	0.472	-0.135	0.140	-0.493	-0.086	-0.130	0.236	...	-0.058	0.095	-0.587	-0.059	-0.097	0.221	-0.887	1.178	-0.001	0.455
AMS SQ Equity	-0.272	0.576	-0.157	0.541	-0.147	0.143	-0.524	-0.088	-0.121	0.422	...	-0.013	0.020	-0.571	-0.062	-0.089	0.280	-0.249	1.202	-0.000	0.479
CS FP Equity	-0.271	0.464	-0.126	0.438	-0.119	0.138	-0.510	-0.084	-0.125	0.241	...	-0.020	0.034	-0.510	-0.050	-0.085	0.167	-0.608	1.163	-0.000	0.459
DG FP Equity	-0.262	0.548	-0.143	0.544	-0.142	0.122	-0.466	-0.111	-0.135	0.323	...	-0.005	0.006	-0.466	-0.063	-0.102	0.211	-0.227	1.324	-0.000	0.460
BNP FP Equity	-0.252	0.568	-0.143	0.545	-0.137	0.137	-0.545	-0.109	-0.130	0.353	...	-0.052	0.086	-0.617	-0.066	-0.096	0.242	-0.721	1.401	-0.001	0.459
BN FP Equity	-0.250	0.299	-0.075	0.315	-0.079	0.090	-0.362	-0.049	-0.063	0.281	...	-0.015	0.026	-0.429	-0.044	-0.058	0.203	-0.473	0.560	-0.000	0.479
ABI BB Equity	-0.229	0.536	-0.123	0.561	-0.129	0.125	-0.546	-0.109	-0.129	0.332	...	-0.067	0.117	-0.670	-0.084	-0.111	0.257	-0.818	1.233	-0.001	0.452
FP FP Equity	-0.222	0.520	-0.116	0.503	-0.112	0.116	-0.521	-0.104	-0.149	0.315	...	-0.030	0.053	-0.613	-0.055	-0.098	0.212	-0.572	1.238	-0.000	0.444
ITX SQ Equity	-0.217	0.415	-0.090	0.376	-0.082	0.081	-0.371	-0.058	-0.077	0.263	...	0.034	-0.026	-0.373	-0.050	-0.062	0.216	-0.116	0.959	-0.000	0.495
ENGI FP Equity	-0.205	0.407	-0.084	0.447	-0.092	0.098	-0.477	-0.066	-0.109	0.250	...	-0.004	0.006	-0.477	-0.050	-0.076	0.196	-0.238	0.944	-0.000	0.481
MUV2 GY Equity	-0.201	0.481	-0.097	0.443	-0.089	0.098	-0.484	-0.074	-0.115	0.288	...	0.208	-0.134	-0.484	-0.047	-0.082	0.192	0.156	1.115	0.000	0.508
ALV GY Equity	-0.187	0.437	-0.082	0.414	-0.078	0.091	-0.487	-0.087	-0.114	0.213	...	-0.001	0.002	-0.487	-0.046	-0.078	0.146	-0.269	1.161	-0.000	0.479
EL FP Equity	-0.155	0.366	-0.057	0.386	-0.060	0.053	-0.342	-0.062	-0.080	0.243	...	0.056	-0.044	-0.352	-0.051	-0.067	0.194	-0.100	0.830	0.000	0.509
SAP GY Equity	-0.151	0.397	-0.060	0.472	-0.071	0.055	-0.366	-0.073	-0.132	0.281	...	0.209	-0.191	-0.366	-0.049	-0.085	0.219	0.161	0.960	0.000	0.517
SAN FP Equity	-0.151	0.272	-0.041	0.270	-0.041	0.035	-0.234	-0.050	-0.063	0.274	...	0.310	-0.288	-0.234	-0.033	-0.048	0.205	0.158	0.550	0.000	0.487
DB1 GY Equity	-0.132	0.355	-0.047	0.360	-0.047	0.049	-0.370	-0.056	-0.091	0.255	...	0.247	-0.176	-0.370	-0.042	-0.063	0.204	0.149	0.747	0.000	0.503
VOW3 GY Equity	-0.093	0.535	-0.050	0.540	-0.050	0.046	-0.496	-0.112	-0.131	0.310	...	0.002	-0.001	-0.530	-0.063	-0.098	0.236	-0.145	1.393	-0.000	0.468
KER FP Equity	-0.082	0.408	-0.034	0.396	-0.033	0.033	-0.402	-0.067	-0.092	0.241	...	0.457	-0.376	-0.414	-0.055	-0.080	0.242	0.499	1.101	0.001	0.512
ADS GY Equity	-0.072	0.420	-0.030	0.428	-0.031	0.031	-0.430	-0.067	-0.100	0.271	...	0.474	-0.328	-0.472	-0.057	-0.075	0.241	0.497	1.002	0.001	0.520
DTE GY Equity	-0.046	0.299	-0.014	0.315	-0.014	0.016	-0.348	-0.052	-0.075	0.181	...	0.179	-0.114	-0.348	-0.043	-0.058	0.153	0.032	0.718	0.000	0.470
CRH ID Equity	-0.043	0.488	-0.021	0.486	-0.021	0.022	-0.517	-0.090	-0.122	0.315	...	0.233	-0.152	-0.523	-0.052	-0.088	0.228	0.195	1.175	0.000	0.487
AI FP Equity	-0.027	0.304	-0.008	0.324	-0.009	0.008	-0.293	-0.057	-0.082	0.192	...	0.546	-0.438	-0.293	-0.039	-0.059	0.142	0.659	0.808	0.000	0.512
RI FP Equity	-0.026	0.280	-0.007	0.280	-0.007	0.008	-0.286	-0.038	-0.059	0.237	...	0.253	-0.170	-0.319	-0.037	-0.047	0.192	0.101	0.596	0.000	0.481
BAS GY Equity	-0.005	0.431	-0.002	0.441	-0.002	0.002	-0.389	-0.067	-0.097	0.221	...	-0.029	0.053	-0.565	-0.054	-0.074	0.171	-0.752	1.188	-0.000	0.444
ENEL IM Equity	0.006	0.379	0.016	0.424	0.014	-0.015	-0.390	-0.058	-0.119	0.250	...	0.661	-0.490	-0.390	-0.040	-0.074	0.198	0.791	0.835	0.001	0.511
LIN GY Equity	0.016	0.363	0.045	0.345	0.047	-0.049	-0.333	-0.060	-0.068	0.183	...	0.509	-0.453	-0.333	-0.050	-0.061	0.173	0.457	0.990	0.000	0.491
VIV FP Equity	0.026	0.325	0.079	0.355	0.072	-0.083	-0.308	-0.067	-0.090	0.251	...	0.305	-0.223	-0.335	-0.046	-0.067	0.196	0.203	0.709	0.000	0.492
BMW GY Equity	0.037	0.454	0.082	0.465	0.080	-0.085	-0.438	-0.083	-0.118	0.251	...	-0.020	0.038	-0.596	-0.054	-0.079	0.192	-0.517	1.152	-0.000	0.476
PHIA NA Equity	0.053	0.324	0.163	0.318	0.166	-0.153	-0.344	-0.049	-0.068	0.258	...	0.509	-0.399	-0.352	-0.046	-0.066	0.208	0.509	0.772	0.000	0.508
VNA GY Equity	0.059	0.319	0.186	0.315	0.188	-0.207	-0.286	-0.056	-0.076	0.300	...	0.500	-0.425	-0.286	-0.043	-0.057	0.241	0.359	0.475	0.000	0.487
AD NA Equity	0.068	0.260	0.261	0.261	0.260	-0.321	-0.211	-0.054	-0.064	0.336	...	0.458	-0.424	-0.233	-0.036	-0.052	0.247	0.259	0.323	0.000	0.504
IBE SQ Equity	0.081	0.322	0.252	0.332	0.244	-0.296	-0.273	-0.049	-0.088	0.230	...	0.984	-0.840	-0.273	-0.038	-0.058	0.188	1.038	0.669	0.001	0.519
NOKIA FH Equity	0.083	0.500	0.165	0.512	0.161	-0.180	-0.459	-0.076	-0.138	0.407	...	-0.012	0.017	-0.616	-0.054	-0.117	0.328	-0.190	0.921	-0.000	0.474
OR FP Equity	0.098	0.298	0.329	0.292	0.337	-0.413	-0.238	-0.057	-0.066	0.227	...	0.770	-0.739	-0.246	-0.038	-0.052	0.180	0.818	0.724	0.001	0.529
MC FP Equity	0.195	0.362	0.540	0.364	0.537	-0.607	-0.322	-0.061	-0.075	0.193	...	0.918	-0.796	-0.344	-0.051	-0.065	0.182	1.316	1.057	0.001	0.532
KNEBV FH Equity	0.212	0.253	0.839	0.265	0.799	-0.960	-0.221	-0.041	-0.043	0.299	...	0.871	-0.707	-0.261	-0.036	-0.040	0.226	0.661	0.450	0.001	0.495
DPW GY Equity	0.246	0.389	0.632	0.420	0.585	-0.574	-0.428	-0.077	-0.099	0.246	...	0.108	-0.065	-0.497	-0.049	-0.073	0.190	-0.014	0.962	0.000	0.515
SU FP Equity	0.264	0.384	0.686	0.420	0.628	-0.762	-0.346	-0.068	-0.101	0.195	...	0.663	-0.578	-0.346	-0.046	-0.073	0.163	1.016	1.095	0.001	0.525
DAI GY Equity	0.284	0.596	0.475	0.567	0.500	-0.563	-0.504	-0.100	-0.143	0.354	...	-0.023	0.041	-0.686	-0.068	-0.104	0.253	-0.372	1.555	-0.000	0.458
SIE GY Equity	0.294	0.412	0.713	0.409	0.719	-0.662	-0.444	-0.068	-0.101	0.203	...	0.345	-0.209	-0.496	-0.048	-0.072	0.159	0.432	1.124	0.000	0.492
PRX NA Equity	0.332	0.403	0.824	0.407	0.816	-1.041	-0.319	-0.060	-0.075	0.378	...	0.571	-0.652	-0.333	-0.059	-0.071	0.340	0.600	0.636	0.001	0.507
ASML NA Equity	0.502	0.405	1.240	0.427	1.175	-1.373	-0.365	-0.069	-0.095	0.281	...	1.116	-1.033	-0.365	-0.050	-0.071	0.234	1.467	1.044	0.001	0.552
FLTR ID Equity	0.510	0.501	1.018	0.490	1.040	-1.147	-0.445	-0.095	-0.129	0.422	...	0.568	-0.448	-0.461	-0.062	-0.094	0.340	0.505	0.825	0.001	0.484
ADYEN NA Equity	1.021	0.391	2.612	0.394	2.594	-4.322	-0.236	-0.055	-0.062	0.411	...	1.567	-1.471	-0.443	-0.063	-0.084	0.665	0.945	0.625	0.003	0.541

50 rows × 28 columns

# normalize data
all_ids = ((all_ids.T - all_ids.T.mean()) / all_ids.T.std()).T

infos = lisa.get_tickers(all_ids.columns)[['gics_sector_name', 'country', 'name']]

from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=5, random_state=0)

pred = kmeans.fit_predict(all_ids.T)

abcd = pd.concat([infos, pd.Series(pred, index=all_ids.columns, name='cluster')], axis=1)

# abcd.sort_values('cluster').to_csv(f'{FOLDER}/cluster.csv', sep=';')
abcd = abcd.sort_values(['cluster', 'gics_sector_name'])
abcd.set_index('cluster', append=True)

# 0 est + proche de 2 Quali / croissance avec LVMH, ASML, OR, mais tempéré par SU et IBE…
# 1 est très financière et cyclique (pas très loin de 3)
# 2 a l'air d'être assez Quali & défensif
# 3 a l'air assez Value, avec des dépendances au secteur aérien, automobile et bancaire
# 4 outlier

		gics_sector_name	country	name
	cluster
FLTR ID Equity	0	Consumer Discretionary	IRELAND	FLUTTER ENTERTAINMENT PLC
MC FP Equity	0	Consumer Discretionary	FRANCE	LVMH MOET HENNESSY LOUIS VUI
PRX NA Equity	0	Consumer Discretionary	NETHERLANDS	PROSUS NV
OR FP Equity	0	Consumer Staples	FRANCE	L'OREAL
KNEBV FH Equity	0	Industrials	FINLAND	KONE OYJ-B
SIE GY Equity	0	Industrials	GERMANY	SIEMENS AG-REG
SU FP Equity	0	Industrials	FRANCE	SCHNEIDER ELECTRIC SE
ASML NA Equity	0	Information Technology	NETHERLANDS	ASML HOLDING NV
IBE SQ Equity	0	Utilities	SPAIN	IBERDROLA SA
BMW GY Equity	1	Consumer Discretionary	GERMANY	BAYERISCHE MOTOREN WERKE AG
ENI IM Equity	1	Energy	ITALY	ENI SPA
FP FP Equity	1	Energy	FRANCE	TOTAL SE
ALV GY Equity	1	Financials	GERMANY	ALLIANZ SE-REG
CS FP Equity	1	Financials	FRANCE	AXA SA
ISP IM Equity	1	Financials	ITALY	INTESA SANPAOLO
MUV2 GY Equity	1	Financials	GERMANY	MUENCHENER RUECKVER AG-REG
BAYN GY Equity	1	Health Care	GERMANY	BAYER AG-REG
BAS GY Equity	1	Materials	GERMANY	BASF SE
CRH ID Equity	1	Materials	IRELAND	CRH PLC
ENGI FP Equity	1	Utilities	FRANCE	ENGIE
DTE GY Equity	2	Communication Services	GERMANY	DEUTSCHE TELEKOM AG-REG
VIV FP Equity	2	Communication Services	FRANCE	VIVENDI
ADS GY Equity	2	Consumer Discretionary	GERMANY	ADIDAS AG
EL FP Equity	2	Consumer Discretionary	FRANCE	ESSILORLUXOTTICA
ITX SQ Equity	2	Consumer Discretionary	SPAIN	INDUSTRIA DE DISENO TEXTIL
KER FP Equity	2	Consumer Discretionary	FRANCE	KERING
AD NA Equity	2	Consumer Staples	NETHERLANDS	KONINKLIJKE AHOLD DELHAIZE N
BN FP Equity	2	Consumer Staples	FRANCE	DANONE
RI FP Equity	2	Consumer Staples	FRANCE	PERNOD RICARD SA
DB1 GY Equity	2	Financials	GERMANY	DEUTSCHE BOERSE AG
PHIA NA Equity	2	Health Care	NETHERLANDS	KONINKLIJKE PHILIPS NV
SAN FP Equity	2	Health Care	FRANCE	SANOFI
DPW GY Equity	2	Industrials	GERMANY	DEUTSCHE POST AG-REG
SAP GY Equity	2	Information Technology	GERMANY	SAP SE
AI FP Equity	2	Materials	FRANCE	AIR LIQUIDE SA
LIN GY Equity	2	Materials	BRITAIN	LINDE PLC
VNA GY Equity	2	Real Estate	GERMANY	VONOVIA SE
ENEL IM Equity	2	Utilities	ITALY	ENEL SPA
DAI GY Equity	3	Consumer Discretionary	GERMANY	DAIMLER AG-REGISTERED SHARES
VOW3 GY Equity	3	Consumer Discretionary	GERMANY	VOLKSWAGEN AG-PREF
ABI BB Equity	3	Consumer Staples	BELGIUM	ANHEUSER-BUSCH INBEV SA/NV
BNP FP Equity	3	Financials	FRANCE	BNP PARIBAS
INGA NA Equity	3	Financials	NETHERLANDS	ING GROEP NV
SAN SQ Equity	3	Financials	SPAIN	BANCO SANTANDER SA
AIR FP Equity	3	Industrials	FRANCE	AIRBUS SE
DG FP Equity	3	Industrials	FRANCE	VINCI SA
SAF FP Equity	3	Industrials	FRANCE	SAFRAN SA
AMS SQ Equity	3	Information Technology	SPAIN	AMADEUS IT GROUP SA
NOKIA FH Equity	3	Information Technology	FINLAND	NOKIA OYJ
ADYEN NA Equity	4	Information Technology	NETHERLANDS	ADYEN NV

viz.easy_plot([exx['ADYEN NA Equity']])

Expliquons les clusters attribués : arbre de décision et forêt aléatoire

new_problem = pd.concat([all_ids.T, abcd['cluster']], axis=1)
X = new_problem.iloc[:,:-1]
y = new_problem.iloc[:, -1]

from sklearn.tree import DecisionTreeClassifier
from sklearn import tree

clf = DecisionTreeClassifier(max_leaf_nodes=8, random_state=0)
clf.fit(X, y)

tree.plot_tree(clf, feature_names=X.columns)
plt.rcParams["figure.figsize"] = (1,1)
plt.show()

Gini mesure l'impureté de la classification : $ G = 1 - \sum_1^n p_i^{2}$

N = 50
1 - (9/N)**2 - (11/N)**2 -(18/N)**2 -(11/N)**2 -(1/N)**2

0.7408000000000001

from sklearn.ensemble import RandomForestClassifier
from sklearn import datasets

# Create decision tree classifer object
clf = RandomForestClassifier(random_state=0, n_jobs=-1)
# Train model
model = clf.fit(X, y)

# Calculate feature importances
importances = model.feature_importances_
# Sort feature importances in descending order
indices = np.argsort(importances)[::-1]

# Rearrange feature names so they match the sorted feature importances
names = X.columns

# Barplot: Add bars
plt.bar(range(X.shape[1]), importances[indices])
# Add feature names as x-axis labels
plt.xticks(range(X.shape[1]), names, rotation=75, fontsize = 8)
# Create plot title
plt.title("Feature Importance")
plt.rcParams["figure.figsize"] = (15,10)
# Show plot
plt.show()

4 - La particularité des données financières

Fortes corrélations

import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

# Generate a large random dataset
d = pd.DataFrame(exx.pct_change())

# Compute the correlation matrix
corr = d.corr()

# Generate a mask for the upper triangle
mask = np.triu(np.ones_like(corr, dtype=bool))

# Set up the matplotlib figure
f, ax = plt.subplots(figsize=(11, 9))

# Generate a custom diverging colormap
cmap = sns.diverging_palette(230, 20, as_cmap=True)

# Draw the heatmap with the mask and correct aspect ratio
sns.heatmap(corr, mask=mask, cmap=cmap, vmax=1, center=0,
            square=True, linewidths=.5, cbar_kws={"shrink": .5})

<matplotlib.axes._subplots.AxesSubplot at 0x7f824e67a2e0>

Séries non stationnaires, non saisonnières, régimes de volatilité

viz.easy_plot(exx.pct_change())